This post is 100% off-grid, powered by batteries.
Yup, the power is out. The UPS is holding up just fine, and this little experiment in tolerance of low quality of electric service appears to be a complete success. When the grid comes back I'm going to check the SOC of my backup and write a final report.
UPDATE: Power was down for approximately 2 hours. I shut down to disconnect the UPS after another hour; battery voltage was 12.74. Unless it was recharging very quickly, it probably had many hours of backup left in it. I need to arrange this setup so I can check the battery's state of charge while it's in operation.... some day.